1. Field of the Invention
Aspects of the present invention relate to batch verification, and more particularly, to a batch verification apparatus and method that can perform batch verification for a plurality of verification values of a plurality of public keys distributed by a plurality of signers.
2. Description of the Related Art
Many encryption schemes have been developed over time to secure information. For example, ElGamal encryption and elliptic curve cryptography (ECC) are utilized to efficiently secure information.
The ElGamal encryption scheme utilizes an exponentiation operation for an encryption process. In addition to the ElGamal encryption scheme, there are many encryption schemes that utilize the exponentiation operation. In the ElGamal encryption scheme, the length of a key (which is an exponent in the exponentiation operation) must be increased by a predetermined length for more stable information security. However, when the length of the key is increased, a magnitude of the exponentiation operation also increases, resulting in a decreased calculation speed. The decrease in the calculation speed more frequently occurs in a mobile device with limited processor capabilities.
Furthermore, the ECC scheme utilizes a coordinates add operation for an encryption process. In the case of the ECC scheme, the length of a key (which is a coefficient to be multiplied by coordinates in the coordinates add operation) also needs to be increased by a predetermined length for more stable information security. However, when the length of the key is increased, a magnitude of the coordinates add operation also increases, resulting in a decreased calculation speed. As in the ECC scheme, the decrease in the calculation speed more frequently occurs in a mobile device with limited processor capabilities.
Also, as the exponentiation operation is slowed in a device performing many exponentiation operations (for example, a router), a bottleneck phenomenon may result. Moreover, a resource-limited device cannot use an encryption function due to many exponentiation operations.
The exponentiation operation, the coordinate addition, and the like, are used for batch verification. Conventional batch verification includes only batch verification of signatures distributed by an identical signer, and excludes batch verification of signatures distributed by another signer. Specifically, only batch verification of signatures having one secret key is performed. Accordingly, a method of performing a quick calculation and performing batch verification of signatures distributed by other signers is needed.